Torque is a measure of the degree to which an influence acting on a body will induce rotation. It can be thought of as the rotational expression of force. Torque comes about as a result of a force being applied to a specific location on a body capable of rotation, such as a lever about a pivot or a globe about a central axis. The strength of a torque is dependent on the angle at which the torque-inducing force is applied. Knowing the correct angle to maximise the torque produced from a given force can prove useful in a variety of engineering and construction applications.
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Things you need
- Trigonometric calculator
Consider the symbolic definition of torque: T = r x F x sin(theta). Here, T represents torque, r represents the distance separating the axis of rotation from where the force is applied, F represents the force, and theta represents the angle at which the force is applied.
To calculate the maximum torque angle, you need to know what value of theta will produce the largest possible value of T for a given force. Since the distance r and the force F are not dependent on theta, you can treat them as constants and essentially ignore them.
Determine what value of theta will produce the largest possible value of sin(theta) as this will in turn produce the largest possible value of T.
Recall that the maximum value of the function sin(theta) is 1.
Determine what angle lends itself to a sine function of value 1. This is called determining the inverse sine of a number. To express this question in a calculator, press the sin^-1, then by 1.
You will get 90 degrees. Applying a force at a 90 degree angle produces the maximum possible torque for that force at that location.
Tips and warnings
- If your calculator is in radians mode, you will get Pi/2 (approximately 1.571) radians instead of 90 degrees. The expressions are equivalent.
- Torque is a vector quantity. When expressing it, always remember to include direction.
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